b. Define a relation SER XR by S ={ (x,y) E R × R |x – y € Z }. Prove that S is an equivalence relation on R.

Q: Let f(x) = r3 on [0, 5]. At x = 27, the Fourier cosine series of f converges to (a) -27 (b) 27 (c) 8...

A: Solution:-

Q: (3) Either prove or provide a counterexample for each of the following statements. I. All scalar mat...

A:

Q: (4) Apply the Fast Modular Exponentiation to find 0 < M < 87, where 5015 = M mod 87.

A:

Q: educe the tollo wing in standard (2-V=10) (I+V(-36)

A: Complex numbers and standard form

Q: (1) If you have been hired at an annual salary of $23,000 and expect to receive annual increases of ...

A: According to bartleby's guidelines, we are allowed to solve only one question at a time. So, the fir...

Q: Question 6 8(x,z) = 2xz+3z-x X-Z Let f(x,z)= Z. 2z2–3 Blank 1: Find the total differential of f(x,z)...

A:

Q: Two charges repel each other with a force of 10µN when they are 20cm apart. What is the force on eac...

A:

Q: 1 -1 is 0-5 The sum of the eigenvalues of the matrix -4

A: An eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes ...

Q: Find the future value of an ordinary annuity if payments are made in the amount R and interest is co...

A: We have to find the future value of ordinary annuity such that R=14000, 4.3% interest compounded qua...

Q: L[ cos? (t) – sin²(t)] = ? %3D 2 S s2 -4 s² +4 2 s2-4 s2+4 O c

A:

Q: 1. Let E be the surface in R³ given by z = e-¤²-y" where x² + y? < 4, oriented with the upward norma...

A:

Q: I. Prove the following statement using the indicated proof. Let r € Z. If r is odd, then (r2 +3)(r² ...

A:

Q: Let C be a closed loop in a plane enclosing an area A. Now consider a point P a distance h from this...

A: The complete solutions are given below  

Q: rotating the given region about the specified line. yA 19-30 Refer to the figure and find the volume...

A:

Q: 3. Let V be a vector space over R with subspaces U and W. (a) Show that U nW is a subspace of V. (b)...

A:

Q: Find the integral of the function f(x,y, z) = x² + y – 2z surface of the unit sphere. over the

A: To find- Find the integral of the function fx, y, z = x2 + y - 2z over the surface of the unit spher...

Q: A small country is comprised of four states, A, B, C, and D. The population of each state is given i...

A: We will round of the standard quota to allocate seats

Q: By using Doolittle's or Cholesky Decomposition method X1 + x2 + x3 = 5 X1 + 2x2 + 2x3 = 6 X1 + 2x2 +...

A:

Q: 1 3 a Let W Span 2 7 If W- = Span b -3 -12 then the value of A is and the value of b is

A: Given- Let W = Span12-3, 37-12.  To find- If W⊥ = Spanab1, then the value of a and the value of b is...

Q: prove the following:

A: Given,           f(x-y, x+y)=2(x2+y2) To prove that,          ∂f(x, y)∂x+∂f(x, y)∂y=2(x+y)

Q: 4

A:

Q: Find equation of plane normal to line = = and pass through line x = y = z.

A: The equation of a plane passing through the point: x0, y0, z0 is defined as ax-x0+by-y0+cz-z0=0, whe...

Q: x-1 y+1 1-z Find equation of plane normal to line 3 == and pass through line x = y = z.

A: The symmetrical form a line that passes through the point: x0, y0, z0 can be represented as x-x0a=y-...

Q: Fill in the blank with an appropriate word, phrase, or symbol(s) for parts a through c. a) The appor...

A: All answers are given below. 

Q: In(k) k k = 1 O converges O diverges

A:

Q: 10. Given vectors ū =[-3,2,–6]and v = [5,0,8], find a) a vector on the x-z plane, and perpendicular ...

A: As per our guidelines I solved first three subparts so kindly request you to repost the remaining qu...

Q: If f(x) = (x +1)²(x² + 5) and g(x) = x° log x, then explain how to find the smallest order Big O est...

A:

Q: c) Is f onto? Answer yes or no and explain. Do not just quote the definition, but give a reason that...

A:

Q: Find the average x-coordinate of a point on the half-torus with the following parametrization (drawn...

A:

Q: Q4) Choose correct answer: rsin-(cosx) i) So S" dy dx = 1-п a. b. -2 1+n C. 2 1+n d. -2

A:  In this problem, we have to evaluate the double integral ∫01∫0sin-1cosxdydx. The limits of integrat...

Q: Show that 1) The columns of a (row-reduced) echelon matrix that contain the non-zero pivots are line...

A:

Q: find periodic interesr rate number of periods of investment 8% compounded quarterly for 9 years

A: Given information The annual interest rate r=8%. Length of investment is 9 years That is t=9 years S...

Q: 3) f = {(0, a), (1, d), (5, e), (9, c)} find the inverse of this function.

A:

Q: For A= {2,x,v} B={w,x} C ={1,2,3} U=- C={1,2,3} U = {1,2,3,4, w, x,y,z} answer the following. Use pr...

A: Solution:-

Q: Find the equation of the sphere with center c= (0, -1, 2) and radius r= 5. O x2 + y + 1)2 + (z + 2)2...

A: Biref answer is given below.

Q: Define f(z)=Arg(z+1). Find all points of continuity. For a point of discontinuity, determine if it i...

A: We know that z=x+iy where x and y real and imaginary part of the complex number.   

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

A:

Q: For A= {2,x,y} B= {w,x} C={1,2,3} U={1,2,3,4,w,x,y,z} Use proper set notation a) C- A AUB c) d) e) f...

A:

Q: P.5 Find the power of the periodic signal x(1) shown below. x(1) 3 2 4/3-241 1 13 4 -2 -3

A:

Q: 2. The total cost of a federal government program in millions of dollars is shown in uue table below...

A: We will use the basic knowledge of cubic splines interpolation to answer this question. Please note ...

Q: A. 28.955° (B, 151.045° C. 30 D. 150° & 3. Two men are just able to lift up a 300 kg weight with a c...

A:

Q: Use the given information to fill in the number of elements for each region in the Venn diagram. n(A...

A:

Q: Problem 2: A piece of string whose length is given bel form an equilateral triangle and the other to...

A: Group (4):-  The length of string is 32 cm. Problem:- A piece of string whose length is 32 cm, is cu...

Q: Q4/ Answer the following (choose one) 1) Find F.T for f(t) = (1-5+(1-sin(21) 2) Find I. F.T for F(@)...

A: We will use the basic knowledge of Fourier transform to answer Question (1) because you have asked u...

Q: 1. Let E be the surface in R³ given by z = e-²-y° where r? + y? < 4, oriented with the upward normal...

A:

Q: If A (0, a) then find A Mult ple Choice (0.0 0), (a, 0, , (0. a 0). 10, a . (a. D, 0). (a. 0. , la, ...

A:

Q: f(x) =x²(3 – 3x)³ 2(3-3x

A: This is the problem of the application of differential Calculus.

Q: 2. Why is (f •g)-' = g¯' of-1? Explain your answer, show mathematical reasoning. (You MUST include a...

A: As we know hoh-1(x) = I(x) 

Q: Question 2: (a) Find all 2 x 2 symmetric matrices that commute with the matrix B = -3 (b) Find all 2...

A:

Q: (a) If z = w-2z, show, without breaking into real and imaginary parts, that 3z = 2w-w. (Hint: take c...

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If yo...